Agricultural activities are a significant contributor to greenhouse gases emissions but strategies to curb these emissions are difficult to implement because of the high inertia in these sectors. In this paper, we investigate from a supply to demand side perspective the stress between food demand and climate change challenges up until 2030 under different patterns of evolution in diets. We use for this purpose GLOBIOM, an applied partial equilibrium model covering, at the world scale and a fine grid resolution, the main land-based sectors: agriculture, forestry and bioenergy. For this exercise, the model is fully linked to a semiflexible endogenous demand system with non-linear Engel’s curves. We examine how more stringent climate change mitigation policies could alter agricultural markets and put at risk nutrition possibilities of populations. The mitigation policies target a similar level of abatment through different sources: limiting deforestation, abating livestock emissions, expanding biofuel production. We show that considering the current dynamic of consumption patterns, these latter policies, if implemented on the supply side directly, could have very uneven effects on the diet across the world and harm primarily developing countries. The severity of impacts will vary according to the future evolution of diet across the world, with more impact for developing regions consuming higher level of ruminant meat and milk. We finally test the robustness of these conclusions to different background diet scenarios, where meat in particular would play a less significant role in future demand.